# Scientific Notation Chapter Questions

**Scientific Notation Chapter Questions**

- What is the purpose of scientific notation?

- When would you use scientific notation?

- How do you convert between standard form and scientific notation?

- How do you compare numbers when they are written in scientific notation?

- How do you multiply and divide numbers in scientific notation?

- How do you add and subtract numbers in scientific notation with the same exponents?

- How do you add and subtract numbers in scientific notation with different exponents?

**Scientific Notation Chapter Problems**

**Purpose of Scientific Notation**

Classwork

- Express the following powers of ten in standard form:
- 101 =
- 102 =
- 103 =
- 104 =
- 105 =

- Express the following answers as powers of 10.
- 103 x 105 =
- 1011 x 106 =
- 1012 x 10-8 =
- 10-4 x 10-7 =
- 10-9 x 103 =

Homework

- Express the following powers of ten in standard form:
- 109 =
- 108 =
- 107 =
- 106 =
- 105 =

- Express the following answers as powers of 10.
- 102 x 104 =
- 103 x 1012 =
- 10-6 x 108 =
- 10-3 x 10-9 =
- 10-7 x 102 =

**How to Write Numbers in Scientific Notation**

Classwork

- Which of the following are correctly written in scientific notation?
- 3.0 x 105
- 0.56 x 109
- 0.103 x 103
- 15 x 10-5
- 5.6 x 10-8
- 4 x 102
- 0.345 x 10-2
- Write each number in scientific notation.
- 13,030,000
- 418,000
- 25,024,000
- 4,500,000
- 20,000
- 870,000,000
- 0.0325
- 0.0000564
- 0.00092
- 0.001002
- 0.00006
- 0.00965784

- Write each number in scientific notation.
- Lightest blue whale: 418,000 lb
- Thinnest glass: 0.00098 in.
- Lightest bird egg:0.0128 oz.
- Diameter of thinnest copper wire: 0.0005 in.
- Mass of Earth’s atmosphere: 5,700,000,000,000,000 tons
- Amount of gold in Earth’s crust: 120,000,000,000,000 metric tons

Homework

- Which of the following are correctly written in scientific notation?
- 0.5 x 104
- 15 x 109
- 3.5567 x 10-7
- 1 x 106
- 5.04 x 10-4
- 0.05 x 10-2
- 6.788432 x 108

- Write each number in scientific notation.
- 4,566,000
- 17,000,300
- 35,000
- 1,078,000,000
- 4,560,700
- 943,000,000,000
- 0.000578
- 0.004598732
- 0.000000558744
- 0.0001000358
- 0.00045805
- 0.000000000000851

- Write each number in scientific notation.
- Mass of smallest insect, a parasitic wasp: 0.00000492 g
- Speed of light: 300,000,000 m/sec
- Mass of a dust particle:0.000000000753 kg
- Distance from Earth to the Sun is approximately: 149,600,000 km
- Earth’s circumference: 40,000,000 m
- Distance between the Sun and Neptune: 4,497,100,000 km

**Converting to Standard Form**

Classwork

- Write each number in standard form.
- Temperature at the Sun’s core: 1.55 x 106 K
- Lowest temperature ever in a lab: 2 x 10-11 K
- Radius of the neon atom is about 3.5 x 10-11 meters
- Radius of Earth’s orbit: 1.5 x 1011 meters
- Avagadro’s number: 6.022 x 1023
- Weight of a paper clip: 1.1 x 10-3 lb.

- Write each number in standard form:
- 7.5 x 105
- 9.765 x 10-10
- 1.27 x 10-8
- 4.56 x 106
- 3.0 x 10-6
- 6.785168 x 108
- 8.00045 x 10-4

PARCC-type Questions:Circle the correct answer

- Which number represents the number 2.3E-4?

a. 230,000

b. 23,000

c. 0.00023

d. 0.000023 - Which number represents the number 6.29E10

a. 6,290,000,000,000

b. 62,900,000,000

c. 0.000000000629

d. 0.0000000000629

Homework

- Write each number in standard form.
- Width of a human hair:7.5 x 10-5 meter
- Distance between Jupiter and the Sun: 4.836 x 1011
- Charge on a Proton/Electron: 1.602176 x 10-19 C
- Faraday constant: 9.649 x 104
- Number of bits on a computer hard disk (as of 2010): 1 x 1013 GB
- Wavelength of green light: 5.5 x 10-7 m

- Write each number in standard form:
- 8.445 x 10-4
- 5.256544 x 109
- 1.0 x 10-5
- 7.45207 x 108
- 2.67 x 10-5
- 6.0005 x 106
- 4.00896 x 10-3

PARCC-type Questions:Circle the correct answer

- Which number represents 6.05E7?

a. 60,500,000

b. 6,050,000,000

c. 0.0000000605

d. 0.000000605 - Which number represents 9.83E-10

a. 9,830,000,000,000

b. 98,300,000,000

c. 0.0000000000983

d. 0.000000000983

Magnitude

Classwork

Write each of the following in scientific notation first, and then indicate the order of magnitude.

- 367______
- 1819.74______
- 5200600 ______
- .00917 ______
- .0363 ______
- .000001 ______
- If M = 624,619,430,000 find the smallest power of 10 that will exceed M.
- If M = 84,973 find the smallest power of 10 that will exceed M.
- If M = 17.196419 find the smallest power of 10 that will exceed M.

Homework

- 7677 ______
- 2489.02 ______
- 4174381 ______
- .00689 ______
- .0002 ______
- .000051 ______
- If M = 8924600043.67 find the smallest power of 10 that will exceed M.
- If M = 3.162 find the smallest power of 10 that will exceed M.
- If M = 4536 find the smallest power of 10 that will exceed M.

**Comparing Numbers in Scientific Notation**

Classwork

- Place the appropriate inequality symbols between the following numbers:
- 9.5 x 1048.2 x 107
- 6.231 x 1072.34 x 103
- 4.567 x 10 -27.32 x 105
- 1.0 x 10-42.0 x 10-5
- 5.66 x 10-76.54 x 10-9
- 8.32 x 10-67.236 x 10-11
- 4.52 x 1047.532 x 104
- 6.5431 x 1086.32 x 108
- 3.5 x 10-61.0 x 10-6
- 4.509 x 10103.45 x 1010

- Order the following sets of numbers from least to greatest.
- 2.3 x 1034.5 x 1057.8 x 1021.3 x 104
- 4.0 x 1095.0 x 1076.0 x 10107.0 x 105
- 4.3 x 1047.5 x 10-21.9 x 1063.3 x 10-4
- 2.5 x 10-125.5 x 10-258.2 x 1029.5 x 10-9
- 5.4 x 1043.2 x 1049.9x 1042.1 x 104
- 9.2 x 10-58.2 x 10-69.2 x 10-68.2 x 10-5

Homework

- Place the appropriate inequality symbols between the following numbers:
- 3.2 x 1064.2 x 109
- 5.41 x 1046.54 x 107
- 9.875 x 10-81.0345 x 108
- 3.0 x 10-64.0 x 10-9
- 4.35 x 10-47.21 x 10-3
- 8.369 x 10-84.1 x 10-13
- 3.98 x 1065.98 x 106
- 1.65 x 1041.56 x 104
- 8.3 x 10-83.0 x 10-8
- 6.8999 x 10157.43 x 1015

- Order the following sets of numbers from least to greatest.
- 4.7 x 1038.9 x 1076.5 x 1056.7 x 104
- 2.0 x 10123.0 x 1064.0 x 1085.0 x 103
- 9.9 x 1055.7 x 10-31.8 x 10-74.4 x 106
- 1.9 x 10-103.6 x 10-69.7 x 1034.5 x 10-23
- 9.3 x 1085.0 x 1088.9x 1086.7 x 108
- 5.5 x 10-74.5 x 10-79.0 x 10-72.7 x 10-7

**Multiplying and Dividing with Scientific Notation**

Classwork

- Evaluate the following. Express the result in scientific notation.
- (3.0 x 10-5)(2.0 x 109)=
- (4.0 x 103)(5.0 x 105)=
- (6.0 x 10-5)(3.0 x 108)=
- (1.5 x 108)(3.2 x 10-4)=
- (2.7 x 10-3)(1.1 x 108)=
- (1.3 x 10-4)(2.0 x 10-6)=
- (8.4 x 106)÷(2.0 x 103)=
- (9.3 x 108)÷(3.0 x 10-2)=
- (5.4 x 1010)÷(2.0 x 104)=
- =
- =
- =

- A tiny space inside a computer chip has been measured to be 2.56 x 10-6 meters wide, 1.4 x 10-7 meters long, and 2.75 x 10-4 meters high. What is its volume?

- In one year about 478 billion telephone calls were placed by 145 million United States telephone subscribers. What was the average number of calls placed per subscriber?

Homework

- Evaluate the following. Express the result in scientific notation.
- (3.0 x 10-5)(3.0 x 108)=
- (4.0 x 102)(4.0 x 107)=
- (7.0 x 10-3)(6.0 x 106)=
- (1.2x 107)(2.2 x 10-3)=
- (2.0 x 10-4)(7.1 x 109)=
- (4.4 x 10-7)(3.0 x 10-3)=
- (6.6x 108)÷(2.0 x 104)=
- (2.7x 106)÷(3.0 x 10-4)=
- (7.5x 1012)÷(2.0 x 105)=
- =
- =
- =

- A tiny space inside another computer chip has been measured to be 3.5 x 10-7 meters wide, 1.8 x 10-8 meters long, and 6.45 x 10-5 meters high. What is its volume?

- The point on a pin has a diameter of approximately 1 x 10-4 meters. If a neon atom has a diameter of about 7.0 x 10-11 meters, about how many neon atoms could fit across the diameter of the point of a pin?

**Adding and Subtracting with Scientific Notation**

Classwork

- Evaluate the following. Express the result in scientific notation.
- (2.1 x 105) + (2.7 x 105)=
- (3.7 x 108) + (4.6 x 108)=
- (6.8 x 10-6) - (3.4 x 10-6)=
- (6.1 x 106) + (3.5 x 107)=
- (8.5 x 1010) - (1.5 x 109)=

- What is the difference between the mass of Earth (5.98 x 1024 kg) and the mass of Venus (4.87 x 1024 kg)?

- What is the difference between the mass of Jupiter (1.90 x 1027 kg) and the mass of Saturn (5.69 x 1026 kg)?

Homework

- Evaluate the following. Express the result in scientific notation.
- (5.8x 109) + (3.1 x 109)=
- (3.5x 106) + (5.8 x 106)=
- (7.5x 10-4) - (4.2 x 10-4)=
- (5.4x 107) + (2.2 x 108)=
- (6.5x 1012) - (3.4 x 1011)=

- What is the difference between the mass of Mars (6.42 x 1023 kg)and the mass of Mercury (3.3 x 1023 kg)?

- What is the difference between the mass of Earth (5.98 x 1024 kg) and the mass of Mars (6.42 x 1023 kg)?

**Scientific Notation Unit Review**

Multiple Choice– Choose the correct answer for each question.

- Which of the following powers of 10 is not correctly written in standard form?
- 105 = 100,000
- 103 = 1,000
- 106 = 1,000,000
- 101 = 1

- Express the following as a power of ten: 10 x 107 =
- 108
- 107
- 106
- 1008

- Express the following as a power of ten: 10-5 x 10-10 =
- 1050
- 10-50
- 10-15
- 1015

- The temperature at the Sun’s core can reach as high as 13,600,000 kelvins. What is this number correctly written in scientific notation?
- 136 x 105
- 1.36 x 107
- 1.36 x 105
- 1.36 x 106

- What is the number .00000002 correctly written in scientific notation?
- 2.0 x 10-8
- 2.0 x 10-9
- 0.2 x 10-8
- 2.0 x 10-10

- What is 4.56 x 105 in standard form?
- 0.00000456
- 0.0000456
- 0.000456
- 456,000

- What is 9 x 106 in standard form?
- 9,000,000
- 90,000,000
- 900,000,000
- 9,800,000,000

- 5.89 x 108 6.4 x 108
- =

- 3.87 x 10-4 5.0 x 10-3
- =

- 7.21 x 107 3.45 x 108
- =

- Which of the following is correctly ordered from greatest to least?
- 2.0 x 1023.0 x 1064.0 x 10-75.0 x 1012
- 4.0 x 10-72.0 x 1023.0 x 1065.0 x 1012
- 3.0 x 1073.0 x 1063.0 x 1023.0 x 10-7
- 4.0 x 10-75.0 x 10122.0 x 1023.0 x 106

- Which of the following is correctly ordered from greatest to least?
- 3.59 x 1064.8 x 1095.4 x 10-56.9 x 10-8
- 5.49 x 10-56.9 x 10-83.5 x 1064.8 x 109
- 6.99 x 10-85.4 x 10-53.5 x 1064.8 x 109
- 1.8 x 1091.5 x 1061.4 x 10-51.9 x 10-8

- (1 x 10-4 )/( 3 x 10-8 ) is approximately
- 3,000
- 30,000
- 300,000
- 333,000

- Identify the number that is not in scientific notation
- 3.2 x 104
- 4.0 x 10
- 52 x 103
- 9 x 10-2

- (4.1 x 103 ) x (1.6 x 10-2) =
- 6.56 x 10
- 6.56 x 105
- 6.56 x 10-5
- 656 x 101

- What is the magnitude of the number 462,000?

- 6
- 3
- 5
- 2

- What is the magnitude of the number .000871
- 6
- -6
- 4
- -4

- If M = 817,004.621, what is the smallest power of 10 that will exceed M?
- 6
- -6
- 3
- 5

**Short Constructed Response**–Write the correct answer for each question. No partial credit will be given.

For problems 19-23, evaluate and express the result in scientific notation.

- (2.0 x 103)(2.0 x 106) =______

- (9 x 10-6) - (3 x 10-6) =______

- (9.6 x 1012)÷(3.2 x 106) =______

- (3.3 x 106) + (6.6 x 106) =______

- (4.2 x 10-1) + (2.4 x 10-1) = ______

**Extended Constructed Response** - Solve the problem, showing all work. Partial credit may be given.

- Your body is creating and killing 15 million red blood cells per second.

- Express 15 million in scientific notation.
- How man red blood cells are created in one hour? Express your answer in scientific notation.
- How many are created in one day? Express your answer in scientific notation.

- There are 18 different animal shapes in the Animal Crackers Cookie Zoo.

- Express this number in scientific notation
- If there are 306 cookies in a package, how many full cookie zoo’s are in the package?
- A case of cookies contains 24 packages. How many sets of animal shapes are there? Express your answer in scientific notation.

- Every day, 20 banks are robbed. The average take is $2,500.

- Express the amount stolen in one robbery in scientific notation.
- Express the average amount stolen in one day in scientific notation.
- Express the average amount stolen in one week in scientific notation.

- A Boeing 747 holds 57,285 gallons of fuel.

- Express the amount of fuel in scientific notation.
- If there are 10 fully fueled Boeing 747s on the tarmac, how much total fuel is in the tanks? Express your answer in scientific notation.
- What is the advantage of using scientific notation for this problem?

Answer Key

**NJ Center for Teaching and Learning ~ 1 ~ **

**Chapter Questions**

- To make very large and very small numbers easier to read and write.
- When you want to write very large numbers small, and very small numbers large.
- Scientific to Standard: Write the coefficient-Add the number of zeros equal to the exponent-Move the decimal the number of places indicated by the exponent.

Standard to Scientific: Write the number without the decimal point-Place the decimal so that the first number is greater than one but less than 10-Count how many places you moved the decimal point; use this as the exponent.

- First, compare the exponents. If the exponents are different, the coefficients do not matter. Whichever number has the lager exponent is the larger number.
- Multiply: Multiply the coefficients. Multiply the powers of ten. Combine those results. Put in proper form.

Divide: Divide the coefficients. Divide the powers of ten. Combine those results. Put in proper form.

- Add or Subtract with same exponents: Add or subtract the coefficients. Rewrite the power of ten. Put in proper form.
- Add or Subtract with different exponents: Rewrite one of the numbers to have the same exponent as the other number. Add or subtract the coefficients. Rewrite the power of ten. Put in proper form.

**Chapter Problems**

- 10
- 100
- 1000
- 10000
- 100000
- 108
- 1017
- 104
- 10-11
- 10-6
- 1000000000
- 100000000
- 10000000
- 1000000
- 100000
- 106
- 1015
- 102
- 10-12
- 10-5
- A, E, F
- 1.303 x 107
- 4.18 x 105
- 2.5024 x 107
- 4.5 x 106
- 2 x 104
- 8.7 x 108
- 3.25 x 10-2
- 5.64 x 10-5
- 9.2 x 10-4
- 1.002 x 10-3
- 6 x 10-5
- 9.65784 x 10-3
- 4.18 x 105
- 9.8 x 10-4
- 1.28 x 10-2
- 5 x 10-4
- 5.7 x 1015
- 1.2 x 1014
- C, D, E, G
- 4.566 x 106
- 1.70003 x 107
- 3.5 x 104
- 1.078 x 109
- 4.5607 x 106
- 9.43 x 1011
- 5.78 x 10-4
- 4.598732 x 10-3
- 5.58744 x 10-7
- 1.000358 x 10-4
- 4.5805 x 10-4
- 8.51 x 10-13
- 4.92 x 10-6
- 3 x 108
- 7.53 x 10-10
- 1.496 x 108
- 4 x 107
- 4.4971 x 109
- 1550000
- .00000000002
- .000000000035
- 150000000000
- 602200000000000000000000
- .0011
- 750000
- .0000000009765
- .0000000127
- 4560000
- .000003
- 678516800
- .000800045
- c
- b
- .000075
- 483600000000
- .0000000000000000001602176
- 96490
- 10000000000000
- .00000055
- .0008445
- 5256544000
- .00001
- 745207000
- .0000267
- 6000500
- .00400896

- a
- d
- 2
- 3
- 6
- -3
- -2
- -6
- 12
- 5
- 2
- 3
- 3
- 6
- -3
- -4
- -5
- 10
- 1
- 4
- 7.8 x 102, 2.3 x 103, 1.3 x 104, 4.5 x 105
- 7.0 x 105, 5.0 x 107, 4.0 x 109, 6.0 x 1010
- 3.3 x 10-4, 7.5 x 10-2, 4.3 x 104, 1.9 x 106
- 5.5 x 10-25, 2.5 x 10-12, 9.5 x 10-9, 8.2 x 102
- 2.1 x 104, 3.2 x 104, 5.4 x 104, 9.9x 104
- 8.2 x 10-6, 9.2 x 10-6,8.2 x 10-5,9.2 x 10-5
- 4.7 x 103, 6.7 x 104, 6.5 x 105, 8.9 x 107
- 5.0 x 103, 3.0 x 106, 4.0 x 108, 2.0 x 1012
- 1.8 x 10-7, 5.7 x 10-3, 9.9 x 105, 4.4 x 106
- 4.5 x 10-23, 1.9 x 10-10, 3.6 x 10-6, 9.7 x 103
- 5.0 x 108, 6.7 x 108, 8.9x 108, 9.3 x 108
- 2.7 x 10-7, 4.5 x 10-7,5.5 x 10-7, 9.0 x 10-7
- 6 x 104
- 2 x 109
- 1.8 x 104
- 4.8 x 104
- 2.97 x 105
- 2.6 x 10-10
- 4.2 x 103
- 3.1 x 1010
- 2.7 x 106
- 3.5 x 10-3
- 5 x 10-5
- 6 x 103
- 9.856 x 10-17
- 3.296 x 103
- 9 x 103
- 1.6 x 1010
- 4.2 x 104
- 2.64 x 104
- 1.42 x 106
- 1.32 x 10-9
- 3.3 x 104
- 9 x 109
- 3.75 x 107
- 2 x 10-10
- 6 x 10-5
- 6 x 105
- 4.0635 x 10-20
- 1.428571 x 106
- 4.8 x 105
- 8.3 x 108
- 3.4 x 10-6
- 4.11 x 107
- 8.35 x 1010
- 1.11 x 1024
- 1.331 x 1027
- 8.9 x 109
- 9.3 x 106
- 3.3 x 10-4
- 2.74 x 108
- 6.16 x 1012
- 3.12 x 1023
- 5.338 x 1024

**NJ Center for Teaching and Learning ~ 1 ~ **

**Unit Review Answer Key**

**NJ Center for Teaching and Learning ~ 1 ~ **

- D
- A
- C
- B
- A
- D
- A
- C
- C
- C
- C
- D
- A
- C
- A
- C
- D
- A
- 4.0 x 109
- 6 x 10-6
- 3 x 106
- 9.9 x 106
- 6.6 x 10-1
- 1.5 x 107

5.4 x 1010

1.296 x 1012

- 1.8 x 10

17

4.08 x 102

- 2.5 x 103

5 x 104

3.5 x 105

- 5.7285 x 104

5.7285 x 105

The mathematical computations can be done mentally.

NJ Center for Teaching and Learning ~ 1 ~